A ‘Back of Envelope Sketch’ for Quintic Design
Last Updated on August 28, 2025 by Editorial Team
Author(s): Greg Oliver
Originally published on Towards AI.
Using the ‘Extended Quadratic Equation’ For Approximating Quintic Architecture
Unlike Quadratics, Cubics and Quartics, Quintic Polynomial architecture y=Ax⁵+Bx⁴+Cx³+Dx²+Ex+F generally produces more ‘polywobbles’ making visualisation less intuitive. While the x Coefficient E and Constant F reveal the gradient and constant at x=0 and though the overall shape replicates a similarly signed +- Cubic from a distance, additional inside Turning Points Tp’s can complicate things a little.
This article discusses the methods used to approximate Turning Points of Quintic Polynomials utilizing the Extended Quadratic Equation. It emphasizes the differences between Quintic behavior compared to lower-order polynomials and presents graphical aids, equations, and techniques for sketching Quintic functions. The author introduces genetic ratios for foundational planning, demonstrating how inner Turning Points can be effectively traced, contributing to improved understanding and design in robotics and higher-order polynomial applications.
Read the full blog for free on Medium.
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